FIA - NLS Models: Biomass vs. Stand Age, G-Reconciled
JAH
2022-10-25
Background
This document has nls (non-linear least squares) regression fits using the LOG-NORMAL functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.
We considered the following Log-Normal functional form \(B = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot biomass interval, which is defined as the measurement time minus 10 years and a 30-year climate normal from 1960-1989, and \(yr\) is the measurement year (all FIA data). Free parameters are \(ge\): biomass growth enhancement over time, \(\alpha\): the growth compensation of lost plot biomass, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(B\), \(c\): the \(StdAge\) value at peak \(B\), and \(d\): the log-normal curve shape parameter.
Model selection is used to determine the best fitting models including \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period) and \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).
model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)
model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)
model 3: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge_{t2} /c \right)} {d} \right]} ^2 \right)\)
Note:
This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval
This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Error in eval(extras, data, env) : object 'P_211' not found
## Error in eval(extras, data, env) : object 'P_211' not found
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_211$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_211.", Mod.Sel1, sep = "")) :
## object 'nls_211.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"212 - Laurentian Mixed Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18747 6234.1
## 2 18742 6234.1 5 0.04459 0.0268 0.9997
## model AIC
## 1 1 195208.2
## 2 2 195169.6
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.236e-01 1.122e-01 2.883 0.00395 **
## phi 0.000e+00 3.737e-03 0.000 1.00000
## a 1.455e+01 5.817e-01 25.018 < 2e-16 ***
## b 8.846e+01 2.713e+00 32.608 < 2e-16 ***
## c 1.392e+02 6.409e+00 21.728 < 2e-16 ***
## d 1.545e+00 4.149e-02 37.235 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5767 on 18742 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (27 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
predict and plot
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7164 1238
## 2 7163 1238 1 -8.6288e-10 0 1
## model AIC
## 1 1 78202.93
## 2 2 78204.93
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.08165 0.11857 0.689 0.491
## a 20.39460 2.05062 9.946 <2e-16 ***
## b 181.88353 10.48899 17.340 <2e-16 ***
## c 170.40292 17.10107 9.964 <2e-16 ***
## d 1.53641 0.08127 18.904 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4157 on 7164 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
predict and plot
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4868 1470.5
## 2 4867 1469.8 1 0.69844 2.3127 0.1284## model AIC
## 1 1 52441.03
## 2 2 52440.72
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.053033 0.214469 -0.247 0.805
## phi 0.014505 0.009861 1.471 0.141
## a 18.601955 1.752549 10.614 <2e-16 ***
## b 122.927550 7.357023 16.709 <2e-16 ***
## c 129.208530 10.051594 12.855 <2e-16 ***
## d 1.259903 0.070683 17.825 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5495 on 4867 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (4 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95381, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -30.683, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8771 1614.1
## 2 8770 1614.1 1 1.3285e-09 0 0.9999
## model AIC
## 1 1 92044.88
## 2 2 92046.88
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.22069 0.09077 -2.431 0.0151 *
## a 25.73594 2.21843 11.601 <2e-16 ***
## b 112.88900 4.17602 27.033 <2e-16 ***
## c 113.57021 6.06064 18.739 <2e-16 ***
## d 1.36021 0.06503 20.918 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.429 on 8771 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (7 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
predict and plot
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12326 3355.8
## 2 12325 3355.8 1 8.5038e-11 0 1
## model AIC
## 1 1 133924.2
## 2 2 133926.2
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.87389 0.11956 7.310 2.85e-13 ***
## a 12.07604 0.64620 18.688 < 2e-16 ***
## b 146.74272 6.48658 22.622 < 2e-16 ***
## c 169.36771 16.98088 9.974 < 2e-16 ***
## d 1.99609 0.06812 29.303 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5218 on 12326 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (16 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
predict and plot
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12425 5068.8
## 2 12424 5065.8 1 3.0036 7.3664 0.006655 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 137933.1
## 2 2 137927.8
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 5.754e-01 1.346e-01 4.275 1.92e-05 ***
## phi 1.604e-02 5.891e-03 2.723 0.00648 **
## a 1.168e+01 7.745e-01 15.075 < 2e-16 ***
## b 1.561e+02 9.184e+00 17.001 < 2e-16 ***
## c 2.015e+02 2.745e+01 7.339 2.28e-13 ***
## d 2.088e+00 8.854e-02 23.577 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6385 on 12424 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (40 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
predict and plot
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1258 341.03
## 2 1257 340.57 1 0.45741 1.6882 0.1941
## model AIC
## 1 1 14066.84
## 2 2 14067.14
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.821e-02 3.664e-01 0.104 0.917
## a 1.252e+01 1.911e+01 0.655 0.512
## b 8.328e+02 2.810e+03 0.296 0.767
## c 5.000e+03 3.947e+04 0.127 0.899
## d 3.188e+00 3.021e+00 1.055 0.292
##
## Residual standard error: 0.5207 on 1258 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96304, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -11.433, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
## Error in nls(f_ln_1, data = G_242, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_242, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_242.", Mod.Sel1, sep = "")) :
## object 'nls_242.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"251 - Prairie Parkland (Temperate)
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1791 389.13
## 2 1790 389.12 1 0.014975 0.0689 0.793
## model AIC
## 1 1 18723.44
## 2 2 18725.38
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.1803 0.2334 -0.772 0.44
## a 26.7896 4.8189 5.559 3.12e-08 ***
## b 101.6305 8.4399 12.042 < 2e-16 ***
## c 104.5991 8.4270 12.412 < 2e-16 ***
## d 1.1194 0.1084 10.324 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4661 on 1791 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9698, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -17.299, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 656 205.66
## 2 655 205.66 1 -1.9804e-10 0 1
## model AIC
## 1 1 6693.871
## 2 2 6695.871
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.7402 0.3111 -2.380 0.017618 *
## a 17.9145 4.7506 3.771 0.000177 ***
## b 86.3366 9.7381 8.866 < 2e-16 ***
## c 67.8705 9.9633 6.812 2.18e-11 ***
## d 1.2644 0.1798 7.031 5.17e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5599 on 656 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94097, p-value = 1.548e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.1924, p-value = 2.56e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
## Error in nls(f_ln_1, data = G_261, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_261, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_261.", Mod.Sel1, sep = "")) :
## object 'nls_261.' not foundsummary
simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit
unable to fit model (only 64 observations)
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"262 - California Dry Steppe
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_262.", Mod.Sel1, sep = "")) :
## object 'nls_262.' not foundsummary
simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit
unable to fit model (0 observations)
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 149 26.638
## 2 148 26.638 1 -3.6088e-11 0 1
## model AIC
## 1 1 1935.134
## 2 2 1937.134
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.224 2.254 0.543 0.5879
## a 0.000 69.109 0.000 1.0000
## b 1000.000 913.184 1.095 0.2753
## c 1898.226 4726.971 0.402 0.6886
## d 2.777 1.518 1.830 0.0693 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4228 on 149 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97748, p-value = 0.0126
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.2016, p-value = 0.0277
## alternative hypothesis: two.sidedpredict and plot
plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Error in nls(f_ln_1, data = G_313, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_313, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_313.", Mod.Sel1, sep = "")) :
## object 'nls_313.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"322 - American Semidesert and Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
- not enough data (only 3 observations)
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 298 169.14
## 2 297 169.14 1 9.3792e-13 0 1
## model AIC
## 1 1 3100.582
## 2 2 3102.582
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.4889 1.4827 0.330 0.7418
## a 0.0000 19.2900 0.000 1.0000
## b 52.4290 27.5134 1.906 0.0577 .
## c 119.8342 66.7961 1.794 0.0738 .
## d 2.1713 1.2242 1.774 0.0771 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7534 on 298 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.8809, p-value = 1.318e-14
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.2814, p-value = 3.356e-10
## alternative hypothesis: two.sidedpredict and plot
plotting 2
* Cannot fit model
332 - Great Plains Steppe
model selection 1
## Error in nls(f_ln_1, data = G_332, start = c(ge = ge.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_332, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_332$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_332.", Mod.Sel1, sep = "")) :
## object 'nls_332.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"- model not fitted because only 62 observations
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"342 - Intermountain Semi-Desert
model selection 1
## Error in nls(f_ln_1, data = G_342, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = G_342, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_342.", Mod.Sel1, sep = "")) :
## object 'nls_342.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"411 - Everglades
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6721 1270.3
## 2 6720 1264.3 1 6.0317 32.06 1.557e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 71115.80
## 2 2 71085.79
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.971e-01 1.651e-01 2.405 0.016185 *
## phi 3.406e-02 6.266e-03 5.435 5.67e-08 ***
## a 9.561e+00 2.760e+00 3.464 0.000536 ***
## b 1.717e+02 1.677e+01 10.241 < 2e-16 ***
## c 2.925e+02 5.966e+01 4.902 9.69e-07 ***
## d 1.911e+00 1.504e-01 12.710 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4337 on 6720 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
predict and plot
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8027 1280.2
## 2 8026 1280.2 1 2.6262e-10 0 1
## model AIC
## 1 1 88546.92
## 2 2 88548.92
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.7642 0.1214 6.294 3.27e-10 ***
## a 31.0606 2.0118 15.439 < 2e-16 ***
## b 118.2933 3.7643 31.425 < 2e-16 ***
## c 106.0278 3.6034 29.424 < 2e-16 ***
## d 1.2855 0.0479 26.839 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3994 on 8027 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
predict and plot
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Error in nls(f_ln_1, data = G_M223, start = c(ge = ge.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_M223, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_M223$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_M223.", Mod.Sel1, sep = "")) :
## object 'nls_M223.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M231 - Ouachita Mixed Forest
model selection 1
## Error in nls(f_ln_1, data = G_M231, start = c(ge = ge.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = G_M231, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in as.formula(formula) : object 'f_ln_3' not found
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_M231$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_M231.", Mod.Sel1, sep = "")) :
## object 'nls_M231.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M242 - Cascade Mixed Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3172 1918.7
## 2 3171 1918.7 1 4.3201e-12 0 1
## model AIC
## 1 1 41988.35
## 2 2 41990.35
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.2910 0.6403 0.454 0.649541
## a 0.0000 7.1556 0.000 1.000000
## b 485.8141 88.9523 5.462 5.08e-08 ***
## c 828.2527 233.3203 3.550 0.000391 ***
## d 2.3429 0.2025 11.569 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7777 on 3172 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94202, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -20.536, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1952 1001.42
## 2 1951 925.67 1 75.745 159.64 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24765.07
## 2 2 24613.15
## 3 3 NAsummary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90919, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.0536, p-value = 0.002261
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M262 - California coastal range - coniferous forest - open woodland - shrub meadow
Model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"- model can fit - but K is negative (only 19 observations) - model excluded
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 356 110.33
## 2 355 109.15 1 1.1717 3.8108 0.05171 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3771.802
## 2 2 3769.947
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.71927 0.37661 -4.565 6.89e-06 ***
## phi 0.05390 0.02373 2.272 0.023713 *
## a 48.59296 14.49239 3.353 0.000886 ***
## b 168.46758 35.84542 4.700 3.73e-06 ***
## c 146.48390 16.95487 8.640 < 2e-16 ***
## d 0.72919 0.12688 5.747 1.96e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5545 on 355 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93581, p-value = 2.293e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.63435, p-value = 0.5259
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1691 583.39
## 2 1690 583.09 1 0.30785 0.8923 0.345
## model AIC
## 1 1 17699.64
## 2 2 17700.75
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.8186 0.3694 -2.216 0.0268 *
## a 25.5229 3.9126 6.523 9.06e-11 ***
## b 117.4741 15.8948 7.391 2.28e-13 ***
## c 225.0966 28.7043 7.842 7.80e-15 ***
## d 1.3310 0.1247 10.676 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5874 on 1691 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (15 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92395, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.869, p-value = 1.122e-06
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2641 1154.9
## 2 2640 1151.5 1 3.4132 7.8251 0.00519 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 28864.48
## 2 2 28858.65
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.47444 0.70178 0.676 0.49906
## phi 0.04074 0.01395 2.919 0.00354 **
## a 20.29162 3.68757 5.503 4.10e-08 ***
## b 100.10614 17.56772 5.698 1.34e-08 ***
## c 222.59104 22.92826 9.708 < 2e-16 ***
## d 1.36913 0.10494 13.047 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6604 on 2640 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89566, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.3736, p-value = 1.222e-05
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1665 654.15
## 2 1664 653.64 1 0.51096 1.3008 0.2542
## model AIC
## 1 1 18742.43
## 2 2 18743.13
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.00819 1.73755 1.156 0.247943
## a 14.15851 4.36299 3.245 0.001197 **
## b 88.92272 26.87216 3.309 0.000956 ***
## c 134.44260 6.30013 21.340 < 2e-16 ***
## d 1.04023 0.05219 19.931 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6268 on 1665 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (5 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93299, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.5759, p-value = 4.742e-06
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 356 147.67
## 2 355 146.35 1 1.3214 3.2053 0.07425 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3622.910
## 2 2 3621.665
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.43327 0.40123 -3.572 0.000403 ***
## phi 0.05965 0.03391 1.759 0.079456 .
## a 4.23809 17.78884 0.238 0.811829
## b 94.02653 28.41884 3.309 0.001034 **
## c 172.96057 97.90646 1.767 0.078156 .
## d 1.81753 0.72623 2.503 0.012774 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6421 on 355 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93172, p-value = 8.478e-12
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.0543, p-value = 1.41e-09
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
## Error in as.formula(formula) : object 'f_ln_3' not found
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 207 64.472
## 2 206 64.472 1 1.1369e-12 0 1
## model AIC
## 1 1 2088.502
## 2 2 2090.502
## 3 3 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.5120 0.5190 -2.913 0.00397 **
## a 24.5523 6.2269 3.943 0.00011 ***
## b 100.9276 22.6252 4.461 1.34e-05 ***
## c 145.9339 14.5564 10.025 < 2e-16 ***
## d 0.8985 0.1519 5.917 1.34e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5581 on 207 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92868, p-value = 1.246e-08
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.78699, p-value = 0.4313
## alternative hypothesis: two.sidedpredict and plot
plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | NA |
| 212 | Laurentian Mixed Forest | 2 |
| 221 | Eastern Broadleaf Forest | 1 |
| 222 | Midwest Broadleaf Forest | 2 |
| 223 | Central Interior Broadleaf Forest | 1 |
| 231 | Southeastern Mixed Forest | 1 |
| 232 | Outer Coastal Plain Mixed Forest | 2 |
| 234 | Lower Mississippi Riverine Forest | 1 |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 1 |
| 255 | Prairie Parkland (Subtropical) | 1 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | 1 |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | 1 |
| 332 | Great Plains Steppe | NA |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 1 |
| M223 | Ozark Broadleaf Forest Meadow | NA |
| M231 | Ouachita Mixed Forest | NA |
| M242 | Cascade Mixed Forest | 1 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 1 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 1 |
| M334 | Black Hills Coniferous Forest | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | 1 |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | alpha | alpha.2.5 | alpha.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6806 | 2847 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 212 | Laurentian Mixed Forest | east | 18775 | 8891 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 221 | Eastern Broadleaf Forest | east | 7170 | 3490 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 222 | Midwest Broadleaf Forest | east | 4877 | 2401 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 223 | Central Interior Broadleaf Forest | east | 8783 | 3725 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 231 | Southeastern Mixed Forest | east | 12347 | 5691 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 232 | Outer Coastal Plain Mixed Forest | east | 12470 | 6101 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 234 | Lower Mississippi Riverine Forest | east | 1265 | 714 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 242 | Pacific Lowland Mixed Forest | pacific | 81 | 81 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1797 | 809 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 255 | Prairie Parkland (Subtropical) | pacific | 663 | 293 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 24 | 24 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 155 | 155 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 215 | 215 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 304 | 240 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 195 | 106 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | interior west | 62 | 62 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 121 | 120 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 93 | 61 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6729 | 2989 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8034 | 3700 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M223 | Ozark Broadleaf Forest Meadow | east | 883 | 343 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M231 | Ouachita Mixed Forest | east | 988 | 481 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | pacific | 3179 | 3176 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1963 | 1963 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 19 | 19 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 362 | 362 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1711 | 1711 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2649 | 2648 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1675 | 1675 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | interior west | 362 | 170 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 213 | 213 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
map #2
plot phi (effect of DeltaPDSI)
plot alpha (biomass compensation effect)
plot a coefficient
## Warning: Removed 36 rows containing missing values (geom_point).
plot b coefficient
## Warning: Removed 36 rows containing missing values (geom_point).
plot c coefficient
## Warning: Removed 36 rows containing missing values (geom_point).
plot d coefficient
## Warning: Removed 36 rows containing missing values (geom_point).
Caclulations - weighted averages
ge (stand biomass enhancement factor in % 2000-2021)
## region weighted.ge
## 1 entire US 0
## 2 pacific 0
## 3 east 0
## 4 interior west 0phi (effect of DeltaPDSI)
## region weighted.phi
## 1 entire US 0
## 2 pacific 0
## 3 east 0
## 4 interior west 0alpha (biomass compensation effect)
## region weighted.alpha
## 1 entire US 0
## 2 pacific 0
## 3 east 0
## 4 interior west 0Calculations - weighted averages subsetted to 15 ecoprovinces
- 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332
ge
## region weighted.ge
## 1 entire US 0
## 2 pacific 0
## 3 east 0
## 4 interior west 0phi
## region weighted.phi
## 1 entire US 0
## 2 pacific 0
## 3 east 0
## 4 interior west 0alpha
## region weighted.alpha
## 1 entire US 0
## 2 pacific 0
## 3 east 0
## 4 interior west 0